Column A is \(\frac{x^44^{-x}}{4^xx^{-4}}\). Then using the properties of exponentials, \(\frac{x^4}{x^{-4}} = x^8\) and \(\frac{4^{-x}}{4^x} = \frac{1}{4^{2x}} = \frac{1}{16^x}\). Thus, column A can be rewritten as \(\frac{x^8}{16^x}\) that is exactly the expression of column B.